Equivariant K-theory ring of the affine Grassmannian as deformation to normal cone
Abstract
We revisit fixed-point localization techniques in equivariant topological K-theory, presenting its fibers over varying points of the equivariant base as cohomology of the corresponding fixed-point schemes. We then employ this framework for an effective description of the equivariant K-theory ring of the affine Grassmannian 𝒢rG. We do so by a detailed study of the relevant fixed points, extending known results to the action of any (x, ζ) ∈ T × 𝔾mrot. We obtain a description of the complexified topological K-theory ring Ktop, 0T× 𝔾mrot(𝒢rG; ℂ) as the ring of functions on a family of affine blowups, extending and proving a conjecture of Roman Bezrukavnikov. While this ring is fairly big, we provide a preferred infinite set of topological generators.
Related
- Equivariant deformation theory and deformations of homogeneous varieties
- Deformation of affine structures and the cohomology of Koszul-Vinberg algebras on the lie groups SO(2), H3(R) and Galilei group SGal(3)
- Involution-equivariant topological recursion and mirror symmetry for the affine binary dihedral Calabi--Yau threefold
- Approximation and extension theorems for normal affine toric varieties
- Gram--Wishart--Stiefel formulation of the N=2, large--d gauge theory in 1D: towards emergent Grassmannian geometry
BibTeX
@misc{lowit2026equivariant,
title = {{Equivariant $K$-theory ring of the affine Grassmannian as deformation to normal cone}},
author = {Jakub Löwit},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12889},
eprint = {2609.12889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12889},
}
RIS
TY - UNPB
TI - Equivariant K-theory ring of the affine Grassmannian as deformation to normal cone
AU - Jakub Löwit
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12889
UR - https://arxiv.org/abs/2609.12889
AB - We revisit fixed-point localization techniques in equivariant topological K-theory, presenting its fibers over varying points of the equivariant base as cohomology of the corresponding fixed-point schemes. We then employ this framework for an effective description of the equivariant K-theory ring of the affine Grassmannian 𝒢r_G. We do so by a detailed study of the relevant fixed points, extending known results to the action of any (x, ζ) ∈ T × 𝔾_m^rot. We obtain a description of the complexified topological K-theory ring K^top, 0_T× 𝔾_m^rot(𝒢r_G; ℂ) as the ring of functions on a family of affine blowups, extending and proving a conjecture of Roman Bezrukavnikov. While this ring is fairly big, we provide a preferred infinite set of topological generators.
ER -